I don't think cyclists are "pulling up on the bars." Cyclists (as in the track cycling example immediately above) are pressing so hard with their legs against gearing so high that they are driving their bodies upward .... they are using leverage off the bars to push or hold their bodies down so the force reacts through the pedals. They are not lifting the bars, they are fighting the resistance with their whole bodies ... effectively driving their bodies down from the bars.
If they were actually lifting the bars they'd wheelie.